Searching for novel two-dimensional (2D) materials is highly desired in the field of nanoelectronics. We here predict a new 2D crystal barium triarsenide (BaAs3) with a series of encouraging functionalities within density functional theory. Being kinetically and thermally stable, the monolayer and bilayer forms of BaAs3 possess narrow indirect band gaps of 0.74eV and 0.34eV, respectively, with high hole mobilities on the order of similar to 10(3)cm(2)V(-1)s(-1). The electronic properties of 2D BaAs3 can be manipulated by controlling the layer thickness. The favorable cleavage energy reveals that layered BaAs3 can be produced as a freestanding 2D material. Furthermore, by introducing vacancy defects monolayer BaAs3 can be transformed from a semiconductor to a metal. Two-dimensional BaAs3 may find promising applications in nanoelectronic devices, such as memristors.